Deep understanding of ordered pairs, Cartesian products, relations, division and coverage of sets, equivalence relations, equivalence classes,
Quotient set, compatibility relation, (maximum) compatibility class, partial order relation, maximal element, minimal element, upper (lower) bound,
Concepts such as supreme (lower) supremacy, maximum (small) element, total order relationship, well-ordered relationship; master the intersection, union,
Operation of difference, complement, and symmetric difference and its operation rules; master the intersection, union, inverse, compound operation and closure of relations
Operation and its properties; master the matrix representation and diagram of relations; deeply understand the reflexivity and anti-reflexivity of relations
To master the method of discrimination of gender, symmetry, antisymmetry and transitivity; master the combination of set coverage and division
Department and distinction; master the discrimination of partial order relations and the drawing method of Hass diagram; be able to find the extremes of a given set in the partial order set
Great Yuan, Minimal Yuan, Upper (Lower) Boundary, Upper (Lower) True Bound, and Largest (Minor) Yuan.
Key points: the nature of the relationship and its discrimination; the compound operation of the relationship and its nature; equivalence relations and equivalence classes,
The relationship between equivalence relations and the division of sets; the discrimination of partial order relations and the drawing method of Hass diagrams, and the particularity of partial order sets
Understanding of location elements.
Difficulty: the transitivity of the relationship and its discrimination; the connection between the equivalence relationship and the division of the set; the partial order relationship
The drawing method of the Hass diagram; the method of finding the elements in the special position in the partial order set.
Chapter 4 Functions
Master the function (mapping), the front domain of the function, the range of the function, the equality of the function, the incidence, the surjection,
Concepts of bijection, identity mapping, inverse function, compound function; master the properties of function compound operations; master function
The difference between the number and the general relationship, the inverse function and the inverse relationship; the proof that the master function is incident, surjective, and bijective;
Grasp the cardinality of sets, the concepts of countable sets and uncountable sets, and the comparison of set cardinality.
Key points: the nature of compound operations; the difference between functions and general relations, inverse functions and inverse relations; functions are
Proof of incident, surjective, and bijective.
Difficulty: The function is the proof of incident, surjective, and bijective.
Chapter 5 Algebraic Structure, Lattice and Boolean Algebra
Master the generations induced by algebraic systems, operations, semigroups, groups, homomorphic mapping, isomorphic mapping, lattice, and lattice
Number system, Boolean algebra, Boolean expressions and other concepts; master the properties of operations and their proofs; be able to prove given
The algebraic system of is a semigroup (or group); master the proof of the isomorphism of two algebraic systems; master the basics of lattice
The principle of nature and lattice duality; master the method of analyzing (conjunct) Boolean expressions in normal form.
Key point: Prove that a given algebraic system is a semigroup (or group); proof that two algebraic systems are isomorphic;
The basic properties of lattices; the analysis (conjunction) of Boolean expressions takes the normal form.
Difficulties: the proof of the isomorphism of two algebraic systems; the analysis (conjunction) of Boolean expressions takes normal form.
Chapter VI Graph Theory
Grasp the degree of graphs, subgraphs, nodes, directed graphs, undirected graphs, multiple graphs, complete graphs, complementary graphs, and raw graphs
To form subgraphs, graph isomorphisms, paths, loops, connected graphs and other concepts and their properties; master the matrix representation of graphs. Palm
Grip trees, directed trees, undirected trees, spanning trees, minimum spanning trees, root trees, roots, leaves, branch points, have
Ordered tree, complete m-ary tree, regular m-ary tree, optimal tree and other concepts; proficient in Kruscal of minimum spanning tree
Algorithm and construction method of optimal binary tree.
Key points: the matrix representation of the graph; the degree of the node and its related properties; tree, directed tree, undirected tree, raw
Tree, minimum spanning tree, root tree, root, leaf, branch point, ordered tree, complete m-ary tree, regular m
Concepts such as fork tree and optimal tree and related properties; several equivalent propositions and proofs about trees; minimum generation
The Kruscal algorithm of the tree and the construction method of the optimal binary tree.
Difficulties: degree of nodes and related properties; Kruscal algorithm of minimum spanning tree and optimal binary tree
The construction method.
4. Requirements for course practice